Ontology without Axioms

Abstract

“Ontology” is here treated as a part of the general theory of logica functions. Approaching ontology as a separate system with its own set of axioms and agreed principles, we avoid difficulties consequent on operating functions having different and varying domains. Such difficulties ought to be solved once and for all within the theory of apparent variables so as to make free operations with functions of different categories possible within the framework of one and the same system of logic. Not expecting essential troubles in the problem of constructing such a theory of apparent variables, and for the time being appealing to intuition as to what can be substituted with respect to which quantifier (A criterion of the meaningfulness of expressions obtained through substitution), the speaker begins to analyse the meaning of a propositional function, i.e., a function which as the result of the substitution of a constant for the variable becomes a sentence. — Consider some expressions of type F(x), e.g.: x is divisible by 5, x is running, it is not true that x, etc. All these expressions attribute some property to x, and when the expression is written in symbols, the property is represented by the symbol placed before the left bracket, that is by the exponent of the function. On the other hand, if we consider the set of all x’s satisfying the expression F(x), then the exponent F may be treated as a symbol of some property common to all these objects, and consequently it may have in symbolic logic a function similar to that of general names in colloquial language.

This is an abstract of Kruszewski’s lecture delivered at the meeting of the Warsaw Institute of Philosophy on December 20, 1924. The report was published by B. Gawecki in “Przeglad Filozoficzny”, Vol. XXVIII (1925) in Polish — see Kruszewski [1925]. Translated from the Polish by Ewa Jansen.